Integrate a power of x times a power of a function of another power of x under that power

[Rafael-SOWNet]

Part of #718.

x^m (sum holding an inverse tangent, inverse hyperbolic tangent or logarithm of x^n)^p, with p ≥ 2, is integrated under t = x^n when (m + 1)/n is whole, which is checked after ToLowestTerms. Before, x^3 (a + b atanh(c x^2))^2 and similar rows ran out of time. The rule is asked just after SolveAPowerOverABinomialInAPowerOfASineOverItsRoots. While merging master, its hunk was re-inserted next to #1922's rule; the two read disjoint shapes.

Rubi chain (master arm at 1e79b0e, 5 s budget):

• Pocket (2,542 rows): master 2,467, this branch 2,478.
• Families 0–8 sampled: identical, apart from one 3.x row that is a timeout on master.
• Moved rows run alone: master solves 0 of 11, the branch 11 of 11. They are 3.4:661 and 670, 5.3.2:115 and 166, and 7.3.2:83, 85, 149, 151, 155, 234 and 296.
• The gate and the suite (15,495 passed) both pass.
• Exact checks at 50 and 300 digits: 120 of 120, including negative x.

On 2.5.0 all eleven were integral(...). The branch answers them in 294 to 2,034 characters, each in under 0.6 s.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura